Question: Solve for $x$ and $y$ using elimination. ${-x+3y = 18}$ ${x+4y = 38}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $7y = 56$ $\dfrac{7y}{{7}} = \dfrac{56}{{7}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-x+3y = 18}\thinspace$ to find $x$ ${-x + 3}{(8)}{= 18}$ $-x+24 = 18$ $-x+24{-24} = 18{-24}$ $-x = -6$ $\dfrac{-x}{{-1}} = \dfrac{-6}{{-1}}$ ${x = 6}$ You can also plug ${y = 8}$ into $\thinspace {x+4y = 38}\thinspace$ and get the same answer for $x$ : ${x + 4}{(8)}{= 38}$ ${x = 6}$